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Evaluate

contexto.140

Solution:

By directly opening this determinant
\begin{array}{l} \cos 65^{\circ} \times \cos 25^{\circ}-\sin 25^{\circ} \times \sin 65^{\circ} \\ =\cos \left(65^{\circ}+25^{\circ}\right) \because \cos A \cos B-\sin A \sin B=\cos (A+B) \\ =\cos 90^{\circ} \\ =0 \\ \because \cos A \cos B-\sin A \sin B=\cos (A+B) \end{array}